A Note on Modified Pell Polynomials

A Note on the Negative Pell Equation

We provide a new elementary proof of a criterion, given in earlier work, for the solvability of the Pell equation x2 −Dy2 = −1 where D is any positive nonsquare integer. Mathematics Subject Classification: Primary 11D09; 11A55; Secondary 11R11; 11R29

A Note on the Modified q-Bernstein Polynomials

A Note on Boole Polynomials

Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials. Finally, we derive some new identities of those poly-nomials from the Witt-type formulas which are related to Euler polynomials.

A Note on Noncommutative Polynomials

1. Introduction. We shall say that an integral domain1 R satisfies condition (M) if any two nonzero elements of R have a nonzero common right multiple. In this note it is proved that if 5 is an extension of a ring R such that S is, roughly speaking, a noncommutative polynomial ring in one variable with R as a coefficient ring, and if R has the property (M), then 5 has property (M). In case R is...

A Note on Barker Polynomials

Properties of Barker polynomials were studied by Turyn and Storer thoroughly in the early sixties, and by Saffari in the late eighties. In the last few years P. Borwein and his collaborators revived interest in the study of Barker polynomials (Barker codes, Barker sequences). In this paper we give a new proof of the fact that there is no Barker polynomial of even degree greater than 12, and hen...